How authentic is the Hadith: "The son of an adulteress will not enter Paradise"? Are there texts that weaken it? And why did Al-Albani mention it in "Silsilat al-Ahadith al-Sahihah" if it is weak?

The Hadith is not authentic, as all its chains of transmission are weak and disturbed in both their isnād (chain of narrators) and matn (text). Some scholars have even ruled it to be fabricated. Those who authenticated the Hadith did not interpret it literally, due to its contradiction with the Almighty’s saying: "And no bearer of burdens will bear the burden of another." They resorted to several interpretations, including: that "the child of zina" refers to someone who commits zina so frequently that they are characterized by it; or that the child of zina will not enter Paradise through the deeds of their parents, unlike the child of a valid marriage; or that the nutfah (sperm/drop) of zina is inherently impure and generally does not result in good, thus, such an individual is not guided to good.